On the other hand, the debate on the differences in the faint-end slope is more complex. In fact, dwarf galaxies can not be merged into the BCG in a reasonable time, since the merging time scale is inversely proportional to the mass of the satellite. A possible explanation is that dwarf galaxies are located in radial orbits passing close to the centre of the cluster. This will result in their disruption, accounting for a part of the missing population. This explanation was also invoked as a possible reason for the high merging rate of FGs. It can also justify the formation of the magnitude gap, since [1]} showed that the merging timescale for satellite on radial orbits is shorter than for tangential ones.
Another possibility is that FGs could lack dwarf galaxies for differences in their accretion time. In fact, [2]} found that the large-scale environment of FGS03 is very rich, so the flat LF found could be explained if the dwarf population are still trapped in nearby groups, awaiting to be merged with the FG. In this context, FGs would be systems in early stages of their mass assembly. We will discuss in more details the large-scale structure of FGs in Sect. REF .
